a) [ : Find the volume of the solid obtained by rotating the region bounded by the lines <

Q: Find the gradient vector of the function f(x,y) =. Select one: O None of the others. - O O + 6xy,…

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Q: Find the slope and y-Intercept (if possible) of the line. (If an answer is undefined, enter…

A: The given equation is 7x-8y=8 We have to find the slope and y-intercept of the given equation.

Q: 1. Find the gradient of the function f(x, y) = x² sin y y.

A: As per the rules we can answer only the first question and rest can be reposted.

Q: The shape of a colony of bacteria on a Petri dish is circular. Find the approximate increase in its…

A: Follow the procedure given below.

Q: Suppose (1, -1) is a critical point of a function f with the continuous second derivatives. If fxx…

A: As we know from the double differentiability test, When rt-s2&gt;0 and r&gt;0 then minima will…

Q: L4Q15. In a display, there are 50 toys in the first row, 45 toys in the second row, and so on in an…

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Q: Consider the function f(x, y) = y ln x - x ln y - . a Find the directional derivative of f at the…

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Q: docs.google.com This option Question * The domain of the function f(x,y)-- x+7-1 D={(x,y) ER² / x² +…

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Q: Compute the directional derivative of the function g(x,y) = sin((5x - 4y)) at the point P(3,3) in…

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Q: Use a triple integral to find the volume of the solid bounded below by the cone z = √x + x² + y² +…

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Q: Q2. Consider the function f: f(x, y) = x² - 4x + y² − 6y ] Find all critical points of f. Find the…

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Q: Find linearly independent functions that are annihilated by the given differential operator. (Give…

A: The characteristics equation is (m-3)(4m+5)=0. So,                   m-34m+5=0⇒m-3=0  or…

Q: L1Q16.Which of the following could be the end behavior of f(x) = -x6 + 3x4 + 8x3 – 4x2 – 6?   f(x) →…

A:

Q: the critical points, local e(s) and sat f(x, y) = 6x+4y+x² + y². Then find the maximum rate of…

A:

Q: Evaluate the line integral along the path C given by x = 4t, y = 8t, where 0 ≤ t ≤ 1. [(x + 3y²) dy…

A: Gievn, x=4t,y=8t And 0≤t≤1

Q: The first term of a geometric sequence is 25 and the second term is 50. Find the common ratio. A.0…

A: topic- geometric sequence r=common ratio=an+1an

Q: L3Q15. Find (g/f) (x), if f(x) = x2 – 4 and g(x) = x – 2. A.x2 – x – 2 B.1/(x + 2)

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Q: Find the limit. Ilm x4 1 5 g B

A: using limit, direct putting value since denominator is polynomial

Q: 3) y(³) − y(¹) = cos(2x). —

A:

Q: Jessica had a loan of $142,000 and made payments of $4,000 at the end of every month to settle it.…

A: In this question, we will use the compound interest formula.

Q: 2. Find the local maximum and minimum values and saddle points (if any) of the function f(x, y) = xy…

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Q: Find a piecewise smooth parametrization of the path C. (ti + tj 0 ≤t≤ 1 r(t) = 1 y 1 ≤t≤2 [y=√x (1,…

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Q: If F = (x² − y² + 2xz)i + (xz − xy + yz)j + (z² + x²)k, find the divergence of - curl F and curl of…

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Q: (a) Find the area of the region bounded by the given curves x+y=0, x = y² + 3y.

A: x+y=0  -----(1)x=-y x=y2+3y ------(2) for points of intersection y2+3y=-yy2+4y=0y(y+4)=0y=0,-4

Q: Solve the length of the unknown side. Round each answer to the nearest tenth. 13 19° 22

A:

Q: How long, to the nearest year, will it take an investment to triple if it is continuously compounded…

A: We can find the required year in the following steps.

Q: The below double integrals are equal: 2 SE S² r cos 0 drd0 = ² r dr Scos e de Select one: O True O…

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Q: The function f(x, y) = 2x² + 4y² + 2x³ has a local maximum at the point (0, 0). Select one: O True O…

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Q: The slope of the tangent line to the curve y = 3 3 at the point (5,2) is: X -

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Q: Consider the function f(x) = x³ + 9x² + 15x. Step 1: Find all values of x that correspond to…

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Q: Given the graph of f'(x) below, where the Domf (x) = (-∞, ∞). Find the interval(s) for which f (x)…

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Q: 1. Find the critical points of the function 2 f(x, y) = x² + 4xy.

A: As per the company guidelines we can solve first question. I hope that the given solution will help…

Q: Evaluate the integral 2 2-x [1² 0 0 xdydx.

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Q: 1) 3 Use reduction of order method with y₁(x) = e³x to find a second solution y2 for the DE: y" - 9y…

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Q: Given f(-6)= 18, f'(-6) = -16, g(-6) = -10, and g' (-6) = 14, find the value of h' (-6) based on the…

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Q: Suppose that f(x) is a continuous function on the interval [-1, 3] with f( − 1) = − 3 and f(3) = 3.…

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Q: 9 outside cardioid r = 1 + cos 0 inside circle r = 3 cos ( 10 lemniscate ² = 4 cos 20 outside r = =…

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Q: Lect one: True False

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Q: If a = (4, 0, 4), b = (3, 4,-4), and c = (0, 4, 5), show that a x (b x c) = (a x b) x c. 60i + 96j -…

A: Solution: Step-1                         Given if a = 4, 0, 4 ,b = 3, 4, -4, and c = 0, 4, 5, show…

Q: y(x) = 4x²y" + y = 0, y(-1) = 6, y'(-1) = 3 , x < 0

A:

Q: 4. Which of the following differential equations has the slope field below 22 ܟ O dy dx dx dx ܔܔܔ…

A: The given slope field is for dydx = -xy . Because slope y'(x) of the solution y(x) is determined…

Q: Find the first three terms of the sequence using the explicit formula 3 × (10)(n -1). A.10, 30, 90…

A: topic - sequence and series

Q: Lateral surface area = Sc C: x² + y² = 64 from (8, 0) to (0,8) f(x, y) = x + y p f(x, y) ds (X, Y)…

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Q: The Integral ffyr² dydx can be written as Select one: O So yx² dady Spa

A: Need to change the order of the integration and select the correct option. Given information: The…

Q: L4Q5. Find the 15th term of the sequence using the explicit formula: 8 × (3)(n - 1). A.38,263,725…

A: The given term is 8 × (3)(n - 1).

Q: Which of the following is NOT a subspace of M22? O O W is the set of matrices of the form and z are…

A: Here is the answer:

Q: Evaluate the line integral along the given path. ds [ (x² + x² +2²) 0₂ C: r(t) = sin(t)i + cos(t)j +…

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Q: Simplify 8logg(64)

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Q: L4Q16. The first term is 4, and the explicit formula is Tn = a + 5(n - 1). Find the 7th term of the…

A: The first term is 4, and the explicit formula is Tn = a + 5(n - 1). Find the 7th term of the…

Q: 17. √ ² √x (x²-3) dx

A: To evaluate the following integral.17 ∫01xx2-3 dx18 ∫-π22π sin x dx